On Universality of Bulk Local Regime of the Deformed Laguerre Ensemble

Details On Universality of Bulk Local Regime of the Deformed Laguerre Ensemble On Universality of Bulk Local Regime of the Deformed Laguerre Ensemble

2009-11-13

arxiv.org/abs/0911.2646v2

Physics

Mathematical Physics

27 pages, 3 figures

Scientific paper

We consider the deformed Laguerre Ensemble $H_n=\dfrac{1}{m}\Sigma_n^{1/2}A_{m,n}A_{m,n}^*\Sigma_n^{1/2}$ in which $\Sigma_n$ is a positive hermitian matrix (possibly random) and $A_{m,n}$ is a $n\times m$ complex Gaussian random matrix (independent of $\Sigma_n$), $\dfrac{m}{n}\to c>1$. Assuming that the Normalized Counting Measure of $\Sigma_n$ converges weakly (in probability) to a non-random measure $N^{(0)}$ with a bounded support we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of $H_n$.

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